Method and Apparatus for Enhancing Object Boundary Precision in an Image

1. A method for enhancing sharpness of object boundaries in an image, comprising: using one or more computers for: receiving an image; computing gradients of color values for pixels in the image; computing displacement vectors for pixels in the image, wherein the magnitude of a displacement vector for a given pixel is proportional to the magnitude of a gradient of a color value at the given pixel; and replacing the color values for pixels, wherein a color value for a given pixel is replaced with a color value obtained from a location at the end of the displacement vector for the given pixel.

2. The method of claim 1 , wherein computing the gradients of color values involves using a discrete differentiation operator.

3. The method of claim 1 , wherein the direction of the displacement vector for a given pixel is determined based on the direction of the gradient and the sign of a second derivative of a color value at the given pixel.

4. The method of claim 1 , wherein if the end of the displacement vector falls between pixels, the method further comprising interpolating color values at the end of the displacement vector based on color values for neighboring pixels around the end of the displacement vector.

5. The method of claim 1 , wherein prior to replacing the color values for the pixels, the method further comprises normalizing the magnitude of the displacement vector so that the largest magnitude among all displacement vectors does not exceed a predetermined maximum.

6. The method of claim 5 , wherein normalizing the magnitude of the displacement vector involves: ranking the magnitude of the displacement vector value among all the displacement vectors; computing a percentile value for the displacement vector based on the associated rank; and normalizing the magnitude of the displacement vector based on the associated percentile value and the magnitude of the displacement vector.

7. The method of claim 6 , wherein computing the percentile value for the displacement vector based on the associated rank involves computing a percentile p=i/N, wherein i is the rank and N is the total number of ranked displacement vectors.

8. The method of claim 2 , wherein the discrete differentiation operator is a Sobel operator.

9. The method of claim 3 , wherein the second derivative of the color value at the given pixel is computed using a Laplacian of Gaussian (LoG) filter.

10. The method of claim 4 , wherein interpolating the color values at the end of the displacement vector involves using a B-spline interpolation.

11. The method of claim 1 , wherein receiving the image involves receiving the image from a video.

12. A computer-readable storage medium storing instructions that when executed by a computer cause the computer to perform a method for enhancing sharpness of object boundaries in an image, the method comprising: receiving an image; computing gradients of color values for pixels in the image; computing displacement vectors for pixels in the image, wherein the magnitude of a displacement vector for a given pixel is proportional to the magnitude of a gradient of a color value at the given pixel; and replacing the color values for pixels, wherein a color value for a given pixel is replaced with a color value obtained from a location at the end of the displacement vector for the given pixel.

13. The computer-readable storage medium of claim 12 , wherein computing gradients of color values involves using a discrete differentiation operator.

14. The computer-readable storage medium of claim 12 , wherein the direction of the displacement vector for a given pixel is determined based on the direction of the gradient and the sign of a second derivative of a color value at the given pixel.

15. The computer-readable storage medium of claim 12 , wherein if the end of the displacement vector falls between pixels, the method further comprising interpolating color values at the end of the displacement vector based on color values for neighboring pixels around the end of the displacement vector.

16. The computer-readable storage medium of claim 12 , wherein prior to replacing the color values for the pixels, the method further comprises normalizing the magnitude of the displacement vector so that the largest magnitude among all displacement vectors does not exceed a predetermined maximum.

17. The computer-readable storage medium of claim 16 , wherein normalizing the magnitude of the displacement vector involves: ranking the magnitude of the displacement vector value among all the displacement vectors; computing a percentile value for the displacement vector based on the associated rank; and normalizing the magnitude of the displacement vector based on the associated percentile value and the magnitude of the displacement vector.

18. The computer-readable storage medium of claim 17 , wherein computing the percentile value for the displacement vector based on the associated rank involves computing a percentile p=I/N, wherein i is the rank and N is the total number of ranked displacement vectors.

19. The computer-readable storage medium of claim 12 , wherein receiving the image involves receiving the image from a video.

20. An apparatus that enhances sharpness of object boundaries in an image, comprising: a processor; a memory; a receiving mechanism configured to receive an image; a computing mechanism coupled to the processor configured to compute gradients of color values for pixels in the image; wherein the computing mechanism is further configured to compute displacement vectors for pixels in the image, wherein the magnitude of a displacement vector for a given pixel is proportional to the magnitude of a gradient of a color value at the given pixel; and a replacement mechanism coupled to the processor configured to replace the color values for pixels, wherein a color value for a given pixel is replaced with a color value obtained from a location at the end of the displacement vector for the given pixel.

21. The apparatus of claim 20 , wherein the computing mechanism is configured to determine the direction of the displacement vector for a given pixel based on the direction of the gradient and the sign of a second derivative of a color value at the given pixel.

22. The apparatus of claim 20 , further comprising an interpolation mechanism configure to interpolate color values at the end of the displacement vector based on color values for neighboring pixels around the end of the displacement vector.

23. The apparatus of claim 20 , further comprising a normalization mechanism configured to normalize the magnitude of the displacement vector so that the largest magnitude among all displacement vectors does not exceed a predetermined maximum.

24. The apparatus of claim 23 , wherein the normalization mechanism is configured to: rank the magnitude of the displacement vector value among all the displacement vectors; compute a percentile value for the displacement vector based on the associated rank; and to normalize the magnitude of the displacement vector based on the associated percentile value and the magnitude of the displacement vector.

25. An apparatus that enhances sharpness of object boundaries in an image, comprising: a processor; a memory; a receiving mechanism configured to receive an image; a computing mechanism coupled to the processor configured to compute gradients of color values for grid points in the image; wherein the computing mechanism is further configured to compute displacement vectors for grid points in the image, wherein the magnitude of a displacement vector for a given grid point is proportional to the magnitude of a gradient of a color value at the grid point; and a replacement mechanism coupled to the processor configured to replace the color values for grid points, wherein a color value for a given grid point is replaced with a color value obtained from a location at the end of the displacement vector for the given grid point.